Carrot Top hustled onstage and quickly turned to the gentleman seated just a few feet to his right.

“This is so exciting, and also awkward,” Carrot Top said, hitting his mark between two opened trunks stuffed with props, “because you said he’s not going to stay, and now he’s staying, and I have all of these jokes. So this is going to be weird.”

The Topper was right about that.

The “he” in this equation was former Vice President Dick Cheney. The stage was Friday’s taping of “The Tonight Show” with Jay Leno, and Carrot Top was part of a polar-opposite booking, introduced just after Leno’s interview with the characteristically stoic Cheney. The former veep was on the show to plug his new memoir “In My Time.”

Carrot Top was plugging nothing but his show at the Luxor. He’d been called on short notice to appear on the same show as Cheney. The Strip comedian has appeared with Leno frequently, but understood instantly that this show would be different.

“They called me, like, two days before, and said, ‘We have Dick Cheney on, and we need someone different and odd and who would be funny,’ ” said Carrot Top (also known by his real name, Scott Thompson) in a phone conversation today. “I am definitely all of that.”

Carrot Top had been told that Cheney would depart the set once he (Carrot Top) launched into his five-minute stand-up segment. But Leno asked Cheney if he’d like to stay to watch the comic bit, and Cheney said “sure.” (For the full appearance, hit this clip and this clip).

“With him sitting there,” Carrot Top noted, “it was like playing the old game show ‘Make Me Laugh.’ ”

Carrot Top had planned to unleash most of his Cheney material on the show, regardless of where the former vice president might be located during the routine.

“It was definitely risky for me to be there anyway, and during rehearsals I pulled out the Cheney stuff,” Carrot Top said. “They were like, ‘Wow, you really want to do that?’ Well, yeah!”

As any viewer still awake after Cheney’s segment could detect, the veteran prop comic was acutely aware of Cheney’s close position, seated less than 10 feet from where Carrot Top was performing.

“I haven’t read your book yet, but I have read George Bush’s book,” Top started, then pulled out a Bush book with Bush’s nose protruding from the cover, Pinocchio-like. He then pulled out a copy of Cheney’s book, which opened to a defibrillator attached. Cheney laughed at that one.

“I wrote all of these jokes last night!” Carrot Top called out.

The Cheney necktie doubling as a stethoscope was well received, as was the “Dick Cheney Shotgun,” with the barrel bent off-target to the right.

“He could probably have me killed, seriously,” Carrot Top said, referring to Cheney. “He could literally have me killed.”

That was it for the Cheney bits. Carrot Top has a half-dozen props dedicated to the former veep. Left out was the Dick Cheney artificial heart, equipped with a dipstick to show when he’s “a quart low.”

“I didn’t want to spend the whole set just ripping him,” Carrot Top said.

The VP did enjoy Topper’s President Obama birth certificate, which was actually an old Etch-A-Sketch where you can shake the surface clean. Cheney laughed, and Top pointed at him in triumph and shouted, “Aaaah, yeah!”

The comic finished off the set with familiar bits -- the mousetrap for gay mice, with a little mirrored disco ball attached; and the rolling carry-on bag that doubles as a Halloween candy sack for fat kids. Then he sat with Leno and Cheney.

“Mr. Vice President,” Leno cracked, “we wanted you to see what torture was actually like.”

“Nice,” Carrot Top said, then turned to Cheney, tossing two of the VP’s books on the table and saying, “It’s too late to get these signed, probably.” Then the comic took a drink from a cup on the table and said, “Your tea is delightful, by the way.”

“That’s not what you were drinking backstage,” Cheney said, getting more laughs than Leno did with his torture joke.

Carrot Top said the vice president was congenial off-camera, asking where the Topper gets his material.